Mantaflow use in blender
The first thing to note is you need to ensure that your domain resolution is set high enough so you have enough fluid detail to fit through any holes. Look at the small cube in the bottom corner of the domain - visible in your second image; that’s the size of one ‘cell’. Any hole smaller than the width of that will definitely obstruct your flow. Start by increasing the Resolution and/or increasing the size of your ‘holes’.
Also, make sure any obstacle meshes are Manifold (completely enclose a volume).